%I #21 Nov 25 2021 08:40:09

%S 1,1,3,6,21,69,342,1791,13419,111924,1306215,17423271,321771366,

%T 6890344533,203170877793,7003940931864,331467832767285,

%U 18429651200703861,1404296660000722446,126080887032762342111,15497512127400670236027,2248516102364654511363948

%N a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 1.

%H G. C. Greubel, <a href="/A135686/b135686.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = a(n-1) + A000045(n)*a(n-1), with a(1) = 1, a(2) = 1.

%p a:= proc(n) option remember; `if`(n<2, n,

%p a(n-2)*(<<0|1>, <1|1>>^n)[1, 2]+a(n-1))

%p end:

%p seq(a(n), n=1..25); # _Alois P. Heinz_, Oct 26 2016

%t RecurrenceTable[{a[1]==1,a[2]==1,a[n]==a[n-1]+Fibonacci[n+1]a[n-2]},a,{n,25}] (* _Harvey P. Dale_, Feb 07 2012 *)

%o (Sage)

%o @CachedFunction

%o def a(n): # A135686

%o if (n<3): return 1

%o else: return a(n-1) + fibonacci(n)*a(n-2)

%o [a(n) for n in (1..40)] # _G. C. Greubel_, Nov 25 2021

%Y Cf. A000045.

%K nonn,less

%O 1,3

%A _Roger L. Bagula_, Feb 18 2008

%E Corrected and edited by _Joerg Arndt_, Oct 26 2016